Beginning with the advent of the laser, dynamic light scattering has proven to be an invaluable technique for determining the dynamic properties of a variety of systems. It has been used to study order-parameter dynamics near the critical points of both pure fluids and binary mixtures. It has proven to be the most accurate method known for determining the diffusion coefficient of macromolecules such as proteins and polymers, as well as that of other particles. Because the radius of a spherical particle can be determined from knowledge of its diffusion coefficient, dynamic light scattering has become an important tool for measuring the size of colloidal particles. It has been determined that light scattered from a collection of particles detected at a point in the far field fluctuates in time as the suspended particles diffuse. The time variation of the intensity of the detected light scattered can be correlated in time to produce an auto-correlation function which gives information concerning the diffusion coefficient of the particles which, in turn, depends upon the diameter of the particle. In practice, measurement of the auto-correlation function is an accurate and reliable method for determining the diffusion coefficient and the diameter of particles in highly dilute systems. In general, the method of dynamic light scattering can be used to measure the dynamic properties of many relatively transparent samples.
Although the use of an auto-correlated signal is known to be useful for highly dilute systems, it has been found that multiple scattering of light in many samples, including more concentrated colloidal suspensions, distorts the measured signal, thus, strongly biasing the determination of the dynamics or diffusion coefficient. For moderately strongly scattering samples, not all of the light scattered leaving the sample is the result of single scattering. Under these conditions, it can be difficult to interpret data in any reliable way. One exception to this situation occurs in the limit of extremely strongly scattering samples, where the photons can be treated as diffusing throughout the sample. In this case, it is possible under certain circumstances to deduce useful information regarding short time scale dynamics of the process giving rise to the scattering.
In an effort to overcome the problem of multiply light scattering, several strategies have been developed. These strategies include calculating the effects of multiple scattering when only few scatterings per incident photon occur, attempting to simulate, via computer, the effects of multiple scattering in the intermediate scattering regime, attempting to calculate the effects of multiple scattering in the diffusing photon limit, and attempting to find scattering geometries in which either multiple scattering or its effects are partially or totally suppressed.
Presently, the best results have been obtained by attempting to suppress the effects of multiple scattering. The most effective experimental method yet devised for dealing with multiple scattering is the cross-correlation technique invented by Phillies. The Phillies method relies on the fact that in order for the incident light to be scattered in a particular direction, the wave vectors of the incident and light scattered must be coupled by that of the dielectric constant fluctuation responsible for the scattering, in a Bragg-like relation, k.sub.inc =k.sub.s .+-.q. Here k.sub.inc is the wave vector of the incident light, k.sub.s is that of the light scattered, and q is the wave vector of the fluctuation responsible for the scattering. Because of this Bragg condition, two different beam-detector combinations can be aligned so as to simultaneously collect light which has been scattered by the same fluctuation. Of course, the two detectors also collect light which has been multiply scattered. This results in detector signals i.sub.A (t) and i.sub.B (t) which arise from both single and multiple scattering contributions. The single scattering contributions are strongly correlated with each other at all times, while the multiple scattering components are only weakly correlated. Measuring the temporal cross-correlation function of the two detector outputs &lt;i.sub.A (.tau.)i.sub.B (0)&gt;, then provides the same information as would be obtained in the single scattering limit using a conventional single-beam, single-detector arrangement to measure &lt;i(.tau.)i(0)&gt;. Although this technique showed promise for determining particle diameters in concentrated solutions, the two-beam, two-detector scattering system is expensive and is difficult to align thereby minimizing the usefulness of such techniques in practice.
In view of the state of the art for determining the dynamic properties of various types of systems, there is a need for a simple, inexpensive and accurate method and apparatus for determining the physical properties of various systems, such as liquid systems having a variety of particle concentrations, and for measuring other types of systems which scatter light.